Theory of Surface Tension. 653 



First, suppose that there is only one independent con- 

 stituent, and that all the molecules are electrically neutral. 

 Let there be n — 1 kinds of molecules S 2 , S 3 , . . . S«, all of 

 which are formed by the polymerization of Sj. In this case 

 there are n—l equations of the type (10), so that there are 

 In equations (9), (10), and (11) determining 2n unknown 

 quantities pi, pj •> ■ • • Pn!, Pi'? p2 ! \ * • • pn" • Hence the 

 constants C in the equations 



WrW =Gi ' li ^ 2 -- nl ■ ■ (12) 



' -F + 2^||=C„ +1 (13) 



become determinate. Since we have supposed that all the 



molecules are electrically neutral, ^r— =0, from which we 



have D = 0, since by our supposition D vanishes at P' and P ;/ . 

 Hence F contains only n unknown quantities /?i, <o 2 , . . . pn for 

 any value of a between a' and a" . But these quantities 

 would have to satisfy n + 1 equations (12) and (13), which is 

 impossible. 



Next, take the case of the system composed of A inde- 

 pendent constituents, the molecules of which are all supposed 

 to be electrically neutral. In this case there are n — li inde- 

 pendent reaction equations of the form (2), to which correspond 

 n — li equations of the type (10). Since we can give any 

 assigned values to p 2 '/p^ \ Ps'/pi', • • • ph/pi between proper 

 limits, 2n unknown quantities p x \ p. 2 ! , . . . p n ', pi", p 2 ", • . . pn" 

 are determinate corresponding to any set of values of 

 p2 / /pi'> • • • Phlpi'j so that C 1? C 2 , . . . C w +i become determinate. 

 Just as in the preceding case in which there is only one 

 independent constituent, the n densities /?,, p 2 , . . . p n would 

 have to satisfy n + 1 equations (12) and (13) in the interior 

 of the transition layer. 



Thus, if we suppose that there are only neutral molecules 

 in the fluids, and also assume that F is independent of a x , then 

 it follows that it is impossible to consider that there would 

 be a transition layer in equilibrium between two fluids. 



Next, suppose that F is again independent of ax, and that 

 there are electrolj tically dissociated molecules. 



First, take the case in which the two fluids consist of only 

 one independent constituent, so called. In this case the 

 molecules S 1? S 2 , • . • S% are connected by n — 2 independent 



